Abstract

There has been much recent work in developing advanced optical metrology methods that use imaging optics for critical dimension measurements and defect detection. Sensitivity to nanometer-scale changes has been observed when measuring critical dimensions of subwavelength 20 nm features or when imaging defects below 15 nm using angle-resolved and focus-resolved optical data. However, these methods inherently involve complex imaging optics and analysis of complicated three-dimensional electromagnetic fields. This paper develops a new approach to enable the rigorous analysis of three-dimensional, through-focus, or angle-resolved optical images. We use rigorous electromagnetic simulation with enhanced Fourier optical techniques, an approach to optical tool normalization, and statistical methods to evaluate sensitivities and uncertainties in the measurement of subwavelength three-dimensional structures.

© 2013 Optical Society of America

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  1. R. M. Silver, B. Barnes, R. Attota, J. Jun, M. Stocker, E. Marx, and H. Patrick, “Scatterfield microscopy to extend the limits of image-based optical metrology,” Appl. Opt. 46, 4248–4257 (2007).
    [CrossRef]
  2. H. Patrick, R. Attota, B. Barnes, T. Germer, R. G. Dixson, M. Stocker, R. M. Silver, and M. Bishop, “Optical critical dimension measurement of silicon grating targets using back focal plane scatterfield microscopy,” J. Microlithogr., Microfabr., Microsyst. 7, 0137011 (2007).
    [CrossRef]
  3. B. M. Barnes, L. P. Howard, J. Jun, P. Lipscomb, and R. M. Silver, “Zero-order imaging of device-sized overlay targets using scatterfield microscopy,” Proc. SPIE 6518, 65180F (2007).
    [CrossRef]
  4. R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, A. Heckert, R. Dixson, T. Germer, and B. Bunday, “Improving optical measurement accuracy using multi-technique nested uncertainties,” Proc. SPIE 7272, 727202 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012

N. F. Zhang, R. M. Silver, H. Zhou, and B. M. Barnes, “Improving optical measurement uncertainty with combined multitool metrology using a Bayesian approach,” Appl. Opt. 51, 6196–6206 (2012).
[CrossRef]

R. M. Silver, J. Qin, B. M. Barnes, H. Zhou, R. Dixson, and F. Goasmat, “Phase sensitive parametric optical metrology: exploring the limits of three-dimensional optical metrology,” Proc. SPIE 8324, 83240N (2012).
[CrossRef]

2011

B. M. Barnes, R. Attota, R. Quintanilha, Y. J. Sohn, and R. M. Silver, “Characterizing a scatterfield optical platform for semiconductor metrology,” Meas. Sci. Technol. 22, 024003 (2011).
[CrossRef]

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, J. Qin, and R. Dixson, “Nested uncertainties to improve measurement accuracy,” Proc. SPIE 7971, 797116 (2011).
[CrossRef]

2009

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, A. Heckert, R. Dixson, T. Germer, and B. Bunday, “Improving optical measurement accuracy using multi-technique nested uncertainties,” Proc. SPIE 7272, 727202 (2009).
[CrossRef]

2007

R. M. Silver, B. Barnes, R. Attota, J. Jun, M. Stocker, E. Marx, and H. Patrick, “Scatterfield microscopy to extend the limits of image-based optical metrology,” Appl. Opt. 46, 4248–4257 (2007).
[CrossRef]

H. Patrick, R. Attota, B. Barnes, T. Germer, R. G. Dixson, M. Stocker, R. M. Silver, and M. Bishop, “Optical critical dimension measurement of silicon grating targets using back focal plane scatterfield microscopy,” J. Microlithogr., Microfabr., Microsyst. 7, 0137011 (2007).
[CrossRef]

B. M. Barnes, L. P. Howard, J. Jun, P. Lipscomb, and R. M. Silver, “Zero-order imaging of device-sized overlay targets using scatterfield microscopy,” Proc. SPIE 6518, 65180F (2007).
[CrossRef]

2006

R. M. Silver, R. Attota, M. Stocker, M. Bishop, J. Jun, E. Marx, M. Davidson, and R. Larrabee, “The limits of image-based optical metrology,” Proc. SPIE 6152, 61520Z (2006).
[CrossRef]

Y. J. Sohn, B. M. Barnes, L. Howard, R. M. Silver, R. Attota, and M. T. Stocker, “Koehler illumination in high-resolution optical metrology,” Proc. SPIE. 6152, 61523S (2006).
[CrossRef]

2005

R. M. Silver, R. Attota, M. Stocker, M. Bishop, L. Howard, T. Germer, E. Marx, M. Davidson, and R. Larrabee, “High-resolution optical metrology,” Proc. SPIE 5752, 67–79 (2005).
[CrossRef]

1995

Attota, R.

B. M. Barnes, R. Attota, R. Quintanilha, Y. J. Sohn, and R. M. Silver, “Characterizing a scatterfield optical platform for semiconductor metrology,” Meas. Sci. Technol. 22, 024003 (2011).
[CrossRef]

R. M. Silver, B. Barnes, R. Attota, J. Jun, M. Stocker, E. Marx, and H. Patrick, “Scatterfield microscopy to extend the limits of image-based optical metrology,” Appl. Opt. 46, 4248–4257 (2007).
[CrossRef]

H. Patrick, R. Attota, B. Barnes, T. Germer, R. G. Dixson, M. Stocker, R. M. Silver, and M. Bishop, “Optical critical dimension measurement of silicon grating targets using back focal plane scatterfield microscopy,” J. Microlithogr., Microfabr., Microsyst. 7, 0137011 (2007).
[CrossRef]

Y. J. Sohn, B. M. Barnes, L. Howard, R. M. Silver, R. Attota, and M. T. Stocker, “Koehler illumination in high-resolution optical metrology,” Proc. SPIE. 6152, 61523S (2006).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, J. Jun, E. Marx, M. Davidson, and R. Larrabee, “The limits of image-based optical metrology,” Proc. SPIE 6152, 61520Z (2006).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, L. Howard, T. Germer, E. Marx, M. Davidson, and R. Larrabee, “High-resolution optical metrology,” Proc. SPIE 5752, 67–79 (2005).
[CrossRef]

Barnes, B.

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, J. Qin, and R. Dixson, “Nested uncertainties to improve measurement accuracy,” Proc. SPIE 7971, 797116 (2011).
[CrossRef]

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, A. Heckert, R. Dixson, T. Germer, and B. Bunday, “Improving optical measurement accuracy using multi-technique nested uncertainties,” Proc. SPIE 7272, 727202 (2009).
[CrossRef]

R. M. Silver, B. Barnes, R. Attota, J. Jun, M. Stocker, E. Marx, and H. Patrick, “Scatterfield microscopy to extend the limits of image-based optical metrology,” Appl. Opt. 46, 4248–4257 (2007).
[CrossRef]

H. Patrick, R. Attota, B. Barnes, T. Germer, R. G. Dixson, M. Stocker, R. M. Silver, and M. Bishop, “Optical critical dimension measurement of silicon grating targets using back focal plane scatterfield microscopy,” J. Microlithogr., Microfabr., Microsyst. 7, 0137011 (2007).
[CrossRef]

Barnes, B. M.

N. F. Zhang, R. M. Silver, H. Zhou, and B. M. Barnes, “Improving optical measurement uncertainty with combined multitool metrology using a Bayesian approach,” Appl. Opt. 51, 6196–6206 (2012).
[CrossRef]

R. M. Silver, J. Qin, B. M. Barnes, H. Zhou, R. Dixson, and F. Goasmat, “Phase sensitive parametric optical metrology: exploring the limits of three-dimensional optical metrology,” Proc. SPIE 8324, 83240N (2012).
[CrossRef]

B. M. Barnes, R. Attota, R. Quintanilha, Y. J. Sohn, and R. M. Silver, “Characterizing a scatterfield optical platform for semiconductor metrology,” Meas. Sci. Technol. 22, 024003 (2011).
[CrossRef]

B. M. Barnes, L. P. Howard, J. Jun, P. Lipscomb, and R. M. Silver, “Zero-order imaging of device-sized overlay targets using scatterfield microscopy,” Proc. SPIE 6518, 65180F (2007).
[CrossRef]

Y. J. Sohn, B. M. Barnes, L. Howard, R. M. Silver, R. Attota, and M. T. Stocker, “Koehler illumination in high-resolution optical metrology,” Proc. SPIE. 6152, 61523S (2006).
[CrossRef]

Bates, D. M.

D. M. Bates and D. G. Watts, Nonlinear Regression Analysis and Its Applications (Wiley, 1998).

Bishop, M.

H. Patrick, R. Attota, B. Barnes, T. Germer, R. G. Dixson, M. Stocker, R. M. Silver, and M. Bishop, “Optical critical dimension measurement of silicon grating targets using back focal plane scatterfield microscopy,” J. Microlithogr., Microfabr., Microsyst. 7, 0137011 (2007).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, J. Jun, E. Marx, M. Davidson, and R. Larrabee, “The limits of image-based optical metrology,” Proc. SPIE 6152, 61520Z (2006).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, L. Howard, T. Germer, E. Marx, M. Davidson, and R. Larrabee, “High-resolution optical metrology,” Proc. SPIE 5752, 67–79 (2005).
[CrossRef]

Bunday, B.

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, A. Heckert, R. Dixson, T. Germer, and B. Bunday, “Improving optical measurement accuracy using multi-technique nested uncertainties,” Proc. SPIE 7272, 727202 (2009).
[CrossRef]

Davidson, M.

R. M. Silver, R. Attota, M. Stocker, M. Bishop, J. Jun, E. Marx, M. Davidson, and R. Larrabee, “The limits of image-based optical metrology,” Proc. SPIE 6152, 61520Z (2006).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, L. Howard, T. Germer, E. Marx, M. Davidson, and R. Larrabee, “High-resolution optical metrology,” Proc. SPIE 5752, 67–79 (2005).
[CrossRef]

Dixson, R.

R. M. Silver, J. Qin, B. M. Barnes, H. Zhou, R. Dixson, and F. Goasmat, “Phase sensitive parametric optical metrology: exploring the limits of three-dimensional optical metrology,” Proc. SPIE 8324, 83240N (2012).
[CrossRef]

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, J. Qin, and R. Dixson, “Nested uncertainties to improve measurement accuracy,” Proc. SPIE 7971, 797116 (2011).
[CrossRef]

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, A. Heckert, R. Dixson, T. Germer, and B. Bunday, “Improving optical measurement accuracy using multi-technique nested uncertainties,” Proc. SPIE 7272, 727202 (2009).
[CrossRef]

Dixson, R. G.

H. Patrick, R. Attota, B. Barnes, T. Germer, R. G. Dixson, M. Stocker, R. M. Silver, and M. Bishop, “Optical critical dimension measurement of silicon grating targets using back focal plane scatterfield microscopy,” J. Microlithogr., Microfabr., Microsyst. 7, 0137011 (2007).
[CrossRef]

Gaylord, T. K.

Germer, T.

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, A. Heckert, R. Dixson, T. Germer, and B. Bunday, “Improving optical measurement accuracy using multi-technique nested uncertainties,” Proc. SPIE 7272, 727202 (2009).
[CrossRef]

H. Patrick, R. Attota, B. Barnes, T. Germer, R. G. Dixson, M. Stocker, R. M. Silver, and M. Bishop, “Optical critical dimension measurement of silicon grating targets using back focal plane scatterfield microscopy,” J. Microlithogr., Microfabr., Microsyst. 7, 0137011 (2007).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, L. Howard, T. Germer, E. Marx, M. Davidson, and R. Larrabee, “High-resolution optical metrology,” Proc. SPIE 5752, 67–79 (2005).
[CrossRef]

Goasmat, F.

R. M. Silver, J. Qin, B. M. Barnes, H. Zhou, R. Dixson, and F. Goasmat, “Phase sensitive parametric optical metrology: exploring the limits of three-dimensional optical metrology,” Proc. SPIE 8324, 83240N (2012).
[CrossRef]

Grann, E. B.

Heckert, A.

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, A. Heckert, R. Dixson, T. Germer, and B. Bunday, “Improving optical measurement accuracy using multi-technique nested uncertainties,” Proc. SPIE 7272, 727202 (2009).
[CrossRef]

Howard, L.

Y. J. Sohn, B. M. Barnes, L. Howard, R. M. Silver, R. Attota, and M. T. Stocker, “Koehler illumination in high-resolution optical metrology,” Proc. SPIE. 6152, 61523S (2006).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, L. Howard, T. Germer, E. Marx, M. Davidson, and R. Larrabee, “High-resolution optical metrology,” Proc. SPIE 5752, 67–79 (2005).
[CrossRef]

Howard, L. P.

B. M. Barnes, L. P. Howard, J. Jun, P. Lipscomb, and R. M. Silver, “Zero-order imaging of device-sized overlay targets using scatterfield microscopy,” Proc. SPIE 6518, 65180F (2007).
[CrossRef]

Jun, J.

B. M. Barnes, L. P. Howard, J. Jun, P. Lipscomb, and R. M. Silver, “Zero-order imaging of device-sized overlay targets using scatterfield microscopy,” Proc. SPIE 6518, 65180F (2007).
[CrossRef]

R. M. Silver, B. Barnes, R. Attota, J. Jun, M. Stocker, E. Marx, and H. Patrick, “Scatterfield microscopy to extend the limits of image-based optical metrology,” Appl. Opt. 46, 4248–4257 (2007).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, J. Jun, E. Marx, M. Davidson, and R. Larrabee, “The limits of image-based optical metrology,” Proc. SPIE 6152, 61520Z (2006).
[CrossRef]

Larrabee, R.

R. M. Silver, R. Attota, M. Stocker, M. Bishop, J. Jun, E. Marx, M. Davidson, and R. Larrabee, “The limits of image-based optical metrology,” Proc. SPIE 6152, 61520Z (2006).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, L. Howard, T. Germer, E. Marx, M. Davidson, and R. Larrabee, “High-resolution optical metrology,” Proc. SPIE 5752, 67–79 (2005).
[CrossRef]

Lipscomb, P.

B. M. Barnes, L. P. Howard, J. Jun, P. Lipscomb, and R. M. Silver, “Zero-order imaging of device-sized overlay targets using scatterfield microscopy,” Proc. SPIE 6518, 65180F (2007).
[CrossRef]

Marx, E.

R. M. Silver, B. Barnes, R. Attota, J. Jun, M. Stocker, E. Marx, and H. Patrick, “Scatterfield microscopy to extend the limits of image-based optical metrology,” Appl. Opt. 46, 4248–4257 (2007).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, J. Jun, E. Marx, M. Davidson, and R. Larrabee, “The limits of image-based optical metrology,” Proc. SPIE 6152, 61520Z (2006).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, L. Howard, T. Germer, E. Marx, M. Davidson, and R. Larrabee, “High-resolution optical metrology,” Proc. SPIE 5752, 67–79 (2005).
[CrossRef]

Moharam, M. G.

Patrick, H.

H. Patrick, R. Attota, B. Barnes, T. Germer, R. G. Dixson, M. Stocker, R. M. Silver, and M. Bishop, “Optical critical dimension measurement of silicon grating targets using back focal plane scatterfield microscopy,” J. Microlithogr., Microfabr., Microsyst. 7, 0137011 (2007).
[CrossRef]

R. M. Silver, B. Barnes, R. Attota, J. Jun, M. Stocker, E. Marx, and H. Patrick, “Scatterfield microscopy to extend the limits of image-based optical metrology,” Appl. Opt. 46, 4248–4257 (2007).
[CrossRef]

Pommet, D. A.

Qin, J.

R. M. Silver, J. Qin, B. M. Barnes, H. Zhou, R. Dixson, and F. Goasmat, “Phase sensitive parametric optical metrology: exploring the limits of three-dimensional optical metrology,” Proc. SPIE 8324, 83240N (2012).
[CrossRef]

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, J. Qin, and R. Dixson, “Nested uncertainties to improve measurement accuracy,” Proc. SPIE 7971, 797116 (2011).
[CrossRef]

Quintanilha, R.

B. M. Barnes, R. Attota, R. Quintanilha, Y. J. Sohn, and R. M. Silver, “Characterizing a scatterfield optical platform for semiconductor metrology,” Meas. Sci. Technol. 22, 024003 (2011).
[CrossRef]

Rao, C. R.

C. R. Rao and H. Toutenburg, Linear Models: Least Squares and Alternatives (Springer, 1995).

Silver, R. M.

R. M. Silver, J. Qin, B. M. Barnes, H. Zhou, R. Dixson, and F. Goasmat, “Phase sensitive parametric optical metrology: exploring the limits of three-dimensional optical metrology,” Proc. SPIE 8324, 83240N (2012).
[CrossRef]

N. F. Zhang, R. M. Silver, H. Zhou, and B. M. Barnes, “Improving optical measurement uncertainty with combined multitool metrology using a Bayesian approach,” Appl. Opt. 51, 6196–6206 (2012).
[CrossRef]

B. M. Barnes, R. Attota, R. Quintanilha, Y. J. Sohn, and R. M. Silver, “Characterizing a scatterfield optical platform for semiconductor metrology,” Meas. Sci. Technol. 22, 024003 (2011).
[CrossRef]

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, J. Qin, and R. Dixson, “Nested uncertainties to improve measurement accuracy,” Proc. SPIE 7971, 797116 (2011).
[CrossRef]

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, A. Heckert, R. Dixson, T. Germer, and B. Bunday, “Improving optical measurement accuracy using multi-technique nested uncertainties,” Proc. SPIE 7272, 727202 (2009).
[CrossRef]

R. M. Silver, B. Barnes, R. Attota, J. Jun, M. Stocker, E. Marx, and H. Patrick, “Scatterfield microscopy to extend the limits of image-based optical metrology,” Appl. Opt. 46, 4248–4257 (2007).
[CrossRef]

H. Patrick, R. Attota, B. Barnes, T. Germer, R. G. Dixson, M. Stocker, R. M. Silver, and M. Bishop, “Optical critical dimension measurement of silicon grating targets using back focal plane scatterfield microscopy,” J. Microlithogr., Microfabr., Microsyst. 7, 0137011 (2007).
[CrossRef]

B. M. Barnes, L. P. Howard, J. Jun, P. Lipscomb, and R. M. Silver, “Zero-order imaging of device-sized overlay targets using scatterfield microscopy,” Proc. SPIE 6518, 65180F (2007).
[CrossRef]

Y. J. Sohn, B. M. Barnes, L. Howard, R. M. Silver, R. Attota, and M. T. Stocker, “Koehler illumination in high-resolution optical metrology,” Proc. SPIE. 6152, 61523S (2006).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, J. Jun, E. Marx, M. Davidson, and R. Larrabee, “The limits of image-based optical metrology,” Proc. SPIE 6152, 61520Z (2006).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, L. Howard, T. Germer, E. Marx, M. Davidson, and R. Larrabee, “High-resolution optical metrology,” Proc. SPIE 5752, 67–79 (2005).
[CrossRef]

Sohn, Y. J.

B. M. Barnes, R. Attota, R. Quintanilha, Y. J. Sohn, and R. M. Silver, “Characterizing a scatterfield optical platform for semiconductor metrology,” Meas. Sci. Technol. 22, 024003 (2011).
[CrossRef]

Y. J. Sohn, B. M. Barnes, L. Howard, R. M. Silver, R. Attota, and M. T. Stocker, “Koehler illumination in high-resolution optical metrology,” Proc. SPIE. 6152, 61523S (2006).
[CrossRef]

Stocker, M.

H. Patrick, R. Attota, B. Barnes, T. Germer, R. G. Dixson, M. Stocker, R. M. Silver, and M. Bishop, “Optical critical dimension measurement of silicon grating targets using back focal plane scatterfield microscopy,” J. Microlithogr., Microfabr., Microsyst. 7, 0137011 (2007).
[CrossRef]

R. M. Silver, B. Barnes, R. Attota, J. Jun, M. Stocker, E. Marx, and H. Patrick, “Scatterfield microscopy to extend the limits of image-based optical metrology,” Appl. Opt. 46, 4248–4257 (2007).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, J. Jun, E. Marx, M. Davidson, and R. Larrabee, “The limits of image-based optical metrology,” Proc. SPIE 6152, 61520Z (2006).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, L. Howard, T. Germer, E. Marx, M. Davidson, and R. Larrabee, “High-resolution optical metrology,” Proc. SPIE 5752, 67–79 (2005).
[CrossRef]

Stocker, M. T.

Y. J. Sohn, B. M. Barnes, L. Howard, R. M. Silver, R. Attota, and M. T. Stocker, “Koehler illumination in high-resolution optical metrology,” Proc. SPIE. 6152, 61523S (2006).
[CrossRef]

Toutenburg, H.

C. R. Rao and H. Toutenburg, Linear Models: Least Squares and Alternatives (Springer, 1995).

Watts, D. G.

D. M. Bates and D. G. Watts, Nonlinear Regression Analysis and Its Applications (Wiley, 1998).

Zhang, N. F.

N. F. Zhang, R. M. Silver, H. Zhou, and B. M. Barnes, “Improving optical measurement uncertainty with combined multitool metrology using a Bayesian approach,” Appl. Opt. 51, 6196–6206 (2012).
[CrossRef]

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, J. Qin, and R. Dixson, “Nested uncertainties to improve measurement accuracy,” Proc. SPIE 7971, 797116 (2011).
[CrossRef]

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, A. Heckert, R. Dixson, T. Germer, and B. Bunday, “Improving optical measurement accuracy using multi-technique nested uncertainties,” Proc. SPIE 7272, 727202 (2009).
[CrossRef]

Zhou, H.

R. M. Silver, J. Qin, B. M. Barnes, H. Zhou, R. Dixson, and F. Goasmat, “Phase sensitive parametric optical metrology: exploring the limits of three-dimensional optical metrology,” Proc. SPIE 8324, 83240N (2012).
[CrossRef]

N. F. Zhang, R. M. Silver, H. Zhou, and B. M. Barnes, “Improving optical measurement uncertainty with combined multitool metrology using a Bayesian approach,” Appl. Opt. 51, 6196–6206 (2012).
[CrossRef]

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, J. Qin, and R. Dixson, “Nested uncertainties to improve measurement accuracy,” Proc. SPIE 7971, 797116 (2011).
[CrossRef]

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, A. Heckert, R. Dixson, T. Germer, and B. Bunday, “Improving optical measurement accuracy using multi-technique nested uncertainties,” Proc. SPIE 7272, 727202 (2009).
[CrossRef]

Appl. Opt.

J. Microlithogr., Microfabr., Microsyst.

H. Patrick, R. Attota, B. Barnes, T. Germer, R. G. Dixson, M. Stocker, R. M. Silver, and M. Bishop, “Optical critical dimension measurement of silicon grating targets using back focal plane scatterfield microscopy,” J. Microlithogr., Microfabr., Microsyst. 7, 0137011 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Meas. Sci. Technol.

B. M. Barnes, R. Attota, R. Quintanilha, Y. J. Sohn, and R. M. Silver, “Characterizing a scatterfield optical platform for semiconductor metrology,” Meas. Sci. Technol. 22, 024003 (2011).
[CrossRef]

Proc. SPIE

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, J. Qin, and R. Dixson, “Nested uncertainties to improve measurement accuracy,” Proc. SPIE 7971, 797116 (2011).
[CrossRef]

B. M. Barnes, L. P. Howard, J. Jun, P. Lipscomb, and R. M. Silver, “Zero-order imaging of device-sized overlay targets using scatterfield microscopy,” Proc. SPIE 6518, 65180F (2007).
[CrossRef]

R. M. Silver, N. F. Zhang, B. Barnes, H. Zhou, A. Heckert, R. Dixson, T. Germer, and B. Bunday, “Improving optical measurement accuracy using multi-technique nested uncertainties,” Proc. SPIE 7272, 727202 (2009).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, J. Jun, E. Marx, M. Davidson, and R. Larrabee, “The limits of image-based optical metrology,” Proc. SPIE 6152, 61520Z (2006).
[CrossRef]

R. M. Silver, R. Attota, M. Stocker, M. Bishop, L. Howard, T. Germer, E. Marx, M. Davidson, and R. Larrabee, “High-resolution optical metrology,” Proc. SPIE 5752, 67–79 (2005).
[CrossRef]

R. M. Silver, J. Qin, B. M. Barnes, H. Zhou, R. Dixson, and F. Goasmat, “Phase sensitive parametric optical metrology: exploring the limits of three-dimensional optical metrology,” Proc. SPIE 8324, 83240N (2012).
[CrossRef]

Proc. SPIE.

Y. J. Sohn, B. M. Barnes, L. Howard, R. M. Silver, R. Attota, and M. T. Stocker, “Koehler illumination in high-resolution optical metrology,” Proc. SPIE. 6152, 61523S (2006).
[CrossRef]

Other

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D. M. Bates and D. G. Watts, Nonlinear Regression Analysis and Its Applications (Wiley, 1998).

US Guide to the Uncertainty of Measurement, American National Standards Institute (1997).

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Figures (13)

Fig. 1.
Fig. 1.

Schematic for a Köhler illuminator. While the general use of Köhler illumination is to illuminate a sample homogeneously even if the source is inhomogeneous, Köhler also permits illumination engineering, such as off-axis illumination, within scatterfield microscopes.

Fig. 2.
Fig. 2.

Maps for the four polarizer–analyzer combinations for each point in the CBFP for the illumination path tool function and complete path function matrices. The color bars for the illumination and complete path are intensities with CCD units, and the color scales on the cross terms (XY and YX) are 103 times smaller than the scales of the other plots. The color bars for collection tool function show the transmissivity of the collection path.

Fig. 3.
Fig. 3.

Method for tool normalization when high-order scattered light is present. Both scattered light angles and polarization states need to be correctly normalized. The top curve shows uncorrected simulation data, and the one below shows the reconstructed image after Fourier normalization.

Fig. 4.
Fig. 4.

(a) Realistic noise spectrum based on experimental data. (b) One example of a noise profile based on the noise spectrum from (a). This noise is added to a simulation to emulate an “experimental” curve.

Fig. 5.
Fig. 5.

Two simulation studies for finite gratings simulated using RCWA at λ=450nm. Each angle scan or through-focus scan consists of 84 concatenated “experimental” profiles, which are noise-added simulated images at various incident angles or focus positions. The center graphs each show the best fit simulation curves for the given “experimental” curves for two orthogonal linear polarizations (in red and blue) at a selected focus or angle position. Parametric uncertainties for both the angle-resolved and focus-resolved simulation studies at 160 nm pitch show less than 1 nm uncertainties (1σ) using this technique.

Fig. 6.
Fig. 6.

Experimental focus-resolved L100P600 lines. The left side and right side data sets show profiles acquired from 400 nm above the substrate to 500 nm below in 100 nm increments.

Fig. 7.
Fig. 7.

Enlargement of one selected focus panel (z=100nm) from Fig. 6 to show the observed sensitivity among the eight dies.

Fig. 8.
Fig. 8.

Experimental angle-resolved L100P600 lines. From left side to right side data sets show profiles acquired at yscan,ypol; yscan,xpol; xscan,ypol; and xscan,xpol.

Fig. 9.
Fig. 9.

Enlargement of angle-resolved experimental data for L100P600 lines from Fig. 8.

Fig. 10.
Fig. 10.

Focus-resolved theory-to-experiment comparisons of the L100P600 target. The focus was varied in 100 nm increments between panels. Two different polarizations are shown in each graph.

Fig. 11.
Fig. 11.

Focus-resolved theory-to-experiment comparisons of the Si single edge target. The focus was varied in 200 nm increments between panels, and 20 panels in total shows focus positions vary from 2 μm below best focus to 2 μm above best focus. Left is for x polarization, and right is for y polarization.

Fig. 12.
Fig. 12.

FM curves for both x polarization (left) and y polarization (right).

Fig. 13.
Fig. 13.

Selected examples at various focus position from the fitting results shown in Fig. 11 with increased error bars.

Equations (6)

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[IPDXX(θ,φ)IPDYX(θ,φ)IPDXY(θ,φ)IPDYY(θ,φ)]=[cosθcosφsinθcosφcosθsinφsinθsinφ]·[PDSS(θ,φ)00PDPP(θ,φ)]·[ASS(θ,φ)APS(θ,φ)ASP(θ,φ)APP(θ,φ)]·[Ixs(θ,φ)Iys(θ,φ)Ixp(θ,φ)Iyp(θ,φ)]·[ExEy].
[ICCDXX(θ,φ)ICCDYX(θ,φ)ICCDXY(θ,φ)ICCDYY(θ,φ)]=[AxxAyxAxyAyy]·[Csx(θ,φ)Cpx(θ,φ)Csy(θ,φ)Cpy(θ,φ)]·[Rrefss(θ,φ)Rrefps(θ,φ)Rrefsp(θ,φ)Rrefpp(θ,φ)]·[Ixs(θ,φ)Iys(θ,φ)Ixp(θ,φ)Iyp(θ,φ)]·[ExEy].
yi=y(xi;a(0))+k=1K[y(xi;a)ak]a=a(0)(akak(0))+εi,
yi=k=1KDik(0)βk(0)+εi
Y(0)=D(0)β(0)+ε.
β^(0)=(D(0)TV1D(0))1D(0)TV1Y(0),

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